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KAM, α -Gevrey regularity and the α -Bruno-Rüssmann condition

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierInstitut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
dc.contributor.authorBounemoura, Abed
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierInstitut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
dc.contributor.authorFéjoz, Jacques
dc.date.accessioned2019-01-11T12:57:19Z
dc.date.available2019-01-11T12:57:19Z
dc.date.issued2017-06
dc.identifier.issn0391-173X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18366
dc.language.isoenen
dc.subjectHamiltonian systemsen
dc.subjectGevrey classen
dc.subjectBruno-R£ussmann vectorsen
dc.subjectstabilityen
dc.subjectKAM theoryen
dc.subject.ddc515en
dc.titleKAM, α -Gevrey regularity and the α -Bruno-Rüssmann conditionen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe prove a new invariant torus theorem, for α-Gevrey smooth Hamiltonian systems , under an arithmetic assumption which we call the α-Bruno-Rüssmann condition , and which reduces to the classical Bruno-Rüssmann condition in the analytic category. Our proof is direct in the sense that, for analytic Hamiltonians, we avoid the use of complex extensions and, for non-analytic Hamiltonians, we do not use analytic approximation nor smoothing operators. Following Bessi, we also show that if a slightly weaker arithmetic condition is not satisfied, the invariant torus may be destroyed. Crucial to this work are new functional estimates in the Gevrey class.en
dc.relation.isversionofjnlnameAnnali della Scuola Normale Superiore di Pisa. Classe di Scienze
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages53en
dc.relation.isversionofdoi10.2422/2036-2145.201707_009en
dc.relation.isversionofjnlpublisherStampacchia Guidoen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingouien
dc.relation.forthcomingprintouien
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-01-11T12:50:47Z
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